Haug and Spavieri have recently presented a new exact solution to Einstein’s field equations. In this paper, we will explore how this new metric could potentially lead to a new model for the cosmos. In the Friedman model, the cosmological constant must be introduced ad-hoc in Einstein’s field equations or, alternatively, directly into the Friedmann equation. However, a similar constant automatically emerges in our cosmological model directly from Einstein’s original 1916 field equations, which initially did not include a cosmological constant. We will analyze this, and it appears that the cosmological constant is little more than an adjustment for the equivalence of the mass-energy of the gravitational field, which is not taken into account in other exact solutions but is addressed in the Haug and Spavieri solution. Our approach seems to indicate that the Hubble sphere can be rep- resented as a black hole, a possibility that has been suggested by multiple authors, but this is a quite different type of black-hole universe that seems to be more friendly than that of a Schwarzschild black-hole.